Question

if the sequence is
2,15,52,125,246....
find the nth term expression
and sum of the nth terms

Answer 1

the growth does not appear exponential, yet it isn't just an easy power, either.

Note that the terms are

2*1, 3*5, 4*13, 5*25, 6*41, ...
The first factor is easy: (n+1)
The second factor is the sequence

1, 5, 13, 25, 41
1st difference: 4,8,12,16, ...
2nd difference: 4,4,4, ...
So, it is a quadratic. Some investigation shows that it is

(n-1)^2 + n^2 = 2n^2-2n+1

So, the nth term is
(n+1)(2n^2-2n+1) = 2n^3-n+1

Now, the sum of then 1st n terms will be a 4th-power polynomial.

So,

Sn = 2∑k^3 - ∑k + ∑1
k=1..n

You probably have handy the needed formulas.